Adding a cold water to tea

This morning i was making a tea. I heated up the water, till it started to boil. Usually instead of filling full cup with very hot water, i fill only half, because the rest i fill with cold water, so the tea is not so hot.
At the moment, when hot water was poured into the cup, i decided to go to check my email. And then suddenly curious question popped up into my mind.

Curious question: In which case the tea will be hotter?
  1. If I add a cold water and go for 5 minutes to check my mail
    or
  2. If I go and check my mail for 5 minutes, and when returned, add a cold water
The answer is not obvious. Because in first case difference between hot tea and room air is greater, and thus energy will flow faster away from the cup. And on the other hand, in the second case the surface between tea and air is greater, so again it means that energy flows faster away.

I did a few calculations to find the answer.



It turns out that it is very important what shape is your cup is in. And also the temperature of cold water may affect the answer. But if you have a cup made out of glass 10cm high, 8cm in diameter, 4mm tight borders, the temperature of hot tea is 70º C, cold water temperature is 15º C, room air temperature is 17º C, then if you add water before you go check email, than cup of tea will loose exactly 17.6% less energy than if you add cold water latter on.

Conclusion. In most cases, if you add water earlier to the tea, you keep your tea hotter, than if you add it latter.

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